Principal Component Analysis Networks and Algorithms

  • Xiangyu Kong
  • Changhua Hu
  • Zhansheng Duan

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 1-16
  3. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 17-46
  4. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 47-73
  5. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 75-110
  6. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 111-148
  7. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 149-184
  8. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 185-233
  9. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 235-279
  10. Xiangyu Kong, Changhua Hu, Zhansheng Duan
    Pages 281-323

About this book

Introduction

This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.

Keywords

PCA Algorithms Principal Component Analysis Feature Extraction Generalized Feature Extraction Neural Networks Singular Component Analysis

Authors and affiliations

  • Xiangyu Kong
    • 1
  • Changhua Hu
    • 2
  • Zhansheng Duan
    • 3
  1. 1.Department of Control EngineeringXi’an Institute of Hi-TechXi’anChina
  2. 2.Department of Control EngineeringXi’an Institute of Hi-TechXi’anChina
  3. 3.Center for Information Engineering Science ResearchXi’an Jiaotong UniversityXi’anChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-2915-8
  • Copyright Information Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-2913-4
  • Online ISBN 978-981-10-2915-8
  • About this book